## Wave breaking in KdV equations with higher nonlinearity

##### Master thesis

##### Permanent lenke

https://hdl.handle.net/11250/3074226##### Utgivelsesdato

2023-05-31##### Metadata

Vis full innførsel##### Samlinger

- Master theses [115]

##### Sammendrag

The undular bore is a wave propagating in shallow water, often resulting from tidal forces that cause a slight change in the wave heights. Favre (1935) did a physical experiment where an undular bore was created and he discovered that the leading wave was breaking when the ratio between the height of the wave above the initial water height and the initial water height exceeded 0.281. He referred to this ratio as the bore strength. This study numerically simulated an undular bore in dimensions and physical assumptions approximating the experiment of Favre to find the threshold for breaking. The nonlinear, dis- persive KdV equation and two extensions of the KdV equation, which we called the eKdV equation and the eeKdV equation, based on the work of Norevik and Kalisch (2022), were utilised to produce the undular bore solutions and the solitary wave solutions. Moreover, the eKdV equation was evaluated with an addition of a background shear flow to analyse if this could improve the result further. The aim was to find an equation that models the breaking of undular bores. The convective breaking criterion was applied on the numerical simulations of the undular bore, where the equation gave a good approximation on undular bore breaking if the bore strength was close to the bore strength found by Favre (1935). The higher-order eKdV and eeKdV equations experienced breaking with a higher bore strength compared to the KdV equation, while the eKdV equation with background vorticity exhibited breaking with an even lower bore strength than the KdV equation. Unfortunately, none of the equations had a lower bore strength than the one achieved by Bjørnestad et al. (2021)